Alternating two-stage methods for consistent linear systems with applications to the parallel solution of Markov chains

Two-stage methods in which the inner iterations are accomplished by an alternating method are developed. Convergence of these methods is shown in the context of solving singular and nonsingular linear systems. These methods are suitable for parallel computation. Experiments related to finding stationary probability distribution of Markov chains are performed. These experiments demonstrate that the parallel implementation of these methods can solve singular systems of linear equations in substantially less time than the sequential counterparts.